Time-frequency perspectives: the 'chirplet' transform

The authors have developed an expansion they call the chirplet transform. It has been successfully applied to a wide variety of signal processing applications, including radar and image processing. There has been a recent debate as to the relative merits of an affine-in-time (wavelet) transform and the classical short-time Fourier transform (STFT) for the analysis of nonstationary phenomena. Chirplet filters embody both the wavelet and STFT as special cases by decoupling the filter bandwidths and center frequencies. Chirplets, by their embodiment of affine geometry in the time-frequency (TF) plane, may also include shears in time and frequency (chirps) and even time-bandwidth product variation (noise bursts) if desired. The most general chirplets may be derived from one or more basic ('mother') chirplets by the transformations or perspective geometry in the TF plane.<>